Question

I need help on how to do this exactly bescsue I have a test soon

Answer 1

Given

we are given a triangle

Here

`\angle1=\angle2`

and they are corresponding angles. so DE is parallel to BC.

`\Rightarrow\angle3=\angle4`

Now in triangles ADE and ABC

we have

`\begin{gathered} \angle1=\angle2 \\ \angle3=\angle4 \end{gathered}`

so by AA criteria the triangles are similar.

Now since triangles are similar their corresponding sides are proportional.

so

`\begin{gathered} (AB)/(AD)=(AC)/(AE)=(BC)/(DE) \\ (x+3)/(x)=(17)/(12)=(y)/(6) \\ \Rightarrow12x+36=17x\text{ and }y=(17)/(2) \\ x=(36)/(5)\text{ and }y=8.5 \\ x=7.2\text{ and }y=8.5 \end{gathered}`

which is the required answer.